G. S. Bisnovatyi-Kogan, R. V. E. Lovelace
In earlier works we pointed out that the disk's surface layers are
non-turbulent and thus highly conducting (or non-diffusive) because the
hydrodynamic and/or magnetorotational (MRI) instabilities are suppressed high
in the disk where the magnetic and radiation pressures are larger than the
plasma thermal pressure. Here, we calculate the vertical profiles of the {\it
stationary} accretion flows (with radial and azimuthal components), and the
profiles of the large-scale, magnetic field taking into account the turbulent
viscosity and diffusivity and the fact that the turbulence vanishes at the
surface of the disk.
Also, here we require that the radial accretion speed be zero at the disk's
surface and we assume that the ratio of the turbulent viscosity to the
turbulent magnetic diffusivity is of order unity. Thus at the disk's surface
there are three boundary conditions. As a result, for a fixed dimensionless
viscosity $\alpha$-value, we find that there is a definite relation between the
ratio ${\cal R}$ of the accretion power going into magnetic disk winds to the
viscous power dissipation and the midplane plasma-$\beta$, which is the ratio
of the plasma to magnetic pressure in the disk. For a specific disk model with
${\cal R}$ of order unity we find that the critical value required for a
stationary solution is $\beta_c \approx 2.4r/(\alpha h)$, where $h$ the disk's
half thickness. For weaker magnetic fields, $\beta > \beta_c$, we argue that
the poloidal field will advect outward while for $\beta< \beta_c$ it will
advect inward. Alternatively, if the disk wind is negligible (${\cal R} \ll
1$), there are stationary solutions with $\beta \gg \beta_c$.
View original:
http://arxiv.org/abs/1110.5196
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